Planets Across Space and Time (PAST). I. Characterizing the Memberships of Galactic Components and Stellar Ages: Revisiting the Kinematic Methods and Applying to Planet Host Stars

Over 4,000 exoplanets have been identified and thousands of candidates are to be confirmed. The relations between the characteristics these planetary systems kinematics, Galactic components, ages their host stars yet well explored. Aiming addressing questions, we conduct a research project, dubbed as PAST (Planets Across Space Time). To do this, one key steps is accurately characterize planet stars. In this paper, Paper I series, revisit kinematic method for classification components extend applicable range velocity ellipsoid from about 100 pc 1, 500 sun in order cover most known hosts. Furthermore, Age-Velocity dispersion Relation (AVR), which allows us derive age with typical uncertainty 10-20% an ensemble Applying above revised methods, present catalog properties (i.e. positions, velocities, relative membership probabilities among thin disk, thick Hercules stream, halo) other basic stellar parameters 2,174 2,872 planets by combining data Gaia, LAMOST, APOGEE, RAVE, NASA exoplanet archive. AVR lay foundation future studies on two dimensions space time context.